Real and complex earthquakes |
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Authors: | Dragomir Saric |
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Affiliation: | Department of Mathematics, The Gradute School and University Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016 |
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Abstract: | We consider (real) earthquakes and, by their extensions, complex earthquakes of the hyperbolic plane . We show that an earthquake restricted to the boundary of is a quasisymmetric map if and only if its earthquake measure is bounded. Multiplying an earthquake measure by a positive parameter we obtain an earthquake path. Consequently, an earthquake path with a bounded measure is a path in the universal Teichmüller space. We extend the real parameter for a bounded earthquake into the complex parameter with small imaginary part. Such obtained complex earthquake (or bending) is holomorphic in the parameter. Moreover, the restrictions to of a bending with complex parameter of small imaginary part is a holomorphic motion of in the complex plane. In particular, a real earthquake path with bounded earthquake measure is analytic in its parameter. |
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Keywords: | Earthquake transverse measure bending |
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